Five-degree-of-freedom heterodyne grating interferometry system

ABSTRACT

A five-degree-of-freedom heterodyne grating interferometry system comprises: a single-frequency laser for emitting single-frequency laser light, the single-frequency laser light can be split into a reference light beam and a measurement light beam; an interferometer lens set and a measurement grating for converting the reference light and the measurement light into a reference interference signal and a measurement interference signal; and multiple optical fiber bundles respectively receiving the measurement interference signal and the reference interference signal, wherein each optical fiber bundle has multiple multi-mode optical fibers respectively receiving interference signals at different positions on the same plane. The system is not over-sensitive to the environment, is small and light, and is easy to arrange. Six-degree-of-freedom ultra-precision measurement can be achieved by arranging multiple five-degree-of-freedom interferometry systems and using redundant information, thereby meeting the needs of a lithography machine worktable for six-degree-of-freedom position and orientation measurement.

TECHNICAL FIELD

The present disclosure relates to the technical field of interferometry,and more specifically, to a five-degree-of-freedom heterodyne gratinginterferometry system.

BACKGROUND ART

As a typical displacement sensor, an interferometry system hasadvantages of traceability to length, high measurement accuracy, largemeasurement range, large dynamic measurement range, easy installationand debugging, etc., and it is widely used in the field of precision andultra-precision measurement, and commonly found in precision machineryand processing equipment. Currently, the interferometry system may bemainly divided into laser interferometry system and gratinginterferometry system. The laser interferometry system is based on themeasurement principle of laser interference. The grating interferometrysystem is based on the principle of diffraction interference, themeasuring basis is grating pitch, and the grating interferometry systemhas a relatively low sensitivity to environmental fluctuations and ahigher repeated measurement accuracy.

Interferometers commonly used in industrial applications can onlyrealize displacement measurement in a single direction. At present, themeasurement accuracy of existing commercial interferometers can usuallyreach the nanometer level and achieve high measurement accuracy.However, in the actual measurement process, it is often affected bygeometric installation errors such as Abbe error and cosine error, whichmay cause inaccurate measurement results; and additional displacementcaused by a small rotation angle due to vibration cannot be avoidedduring the movement. With the continuous development of precisionmachinery, and continuous improvement of the motion indicators such asmeasurement accuracy, measurement distance and measurement speed and soon, the need for multi-degree-of-freedom measurement is graduallyincreasing, for example, in a position measurement system of anultra-precision worktable of lithography machine.

To solve the above problems, conventional methods use a distributedmulti-degree-of-freedom measurement system composed of severalsingle-degree-of-freedom laser measurement systems. For example, USpatent U.S. Pat. No. 6,020,964B2 (published on Feb. 1, 2000) from ASMLof the Netherlands, US patent U.S. Pat. No. 6,980,279B2 (published onDec. 27, 2005) from Nikon of Japan, and US patent U.S. Pat. No.7,355,719B2 (published on Apr. 8, 2008) from Agilent of the UnitedStates all use similar six-degree-of-freedom measurement systems, thatis, a multi-axis laser interferometer is arranged in a horizontaldirection, a measurement light is introduced into the Z axis using a 45°reflector, the reflector is mounted on the side and in Z direction, arotation angle is calculated by using the displacement difference, andthus six-degree-of-freedom measurement is realized. However, thedistributed interferometry system takes up a lot of space and isdifficult to install and adjust, thus cannot meet the measurementrequirements. In the grating interferometry system, atwo-degree-of-freedom measurement system is commonly used, for example,in US patent US0058173A1 (published on Mar. 15, 2007) from Heidenhain ofGermany but cannot achieve simultaneous measurement of more degrees offreedom. Other grating interferometry systems, such as [C. B. Lee, G. H.Kim, and S. K. Lee, “Design and construction of a single unitmulti-function optical encoder for a six-degree-of-freedom motion errormeasurement in an ultra-precision linear stage”, Meas. Sci. Technol,2011], a simple method for simultaneous measurement ofsix-degree-of-freedom proposed by Lee, etc. using PSD and a specificlight path structure based on a two-degree-of-freedom gratinginterferometry system, have a more complex structure of the measurementsystem, the measurement of multi-degree of freedom depends on thespecific light path structure, measurement consistency and stability arepoor, the measurement accuracy is largely limited by the performance ofa detector, and generally the rotation angle measurement accuracy canonly reach an order of arc seconds, and the displacement measurementaccuracy can only reach an order of micrometers, which is difficult tomeet the performance requirements of ultra-precision measurementsystems.

SUMMARY

In consideration of the limitations of the above-mentioned technicalsolutions, a precise five-degree-of-freedom heterodyne gratinginterferometry system, which has advantages such as simple and compactoptical structure, easy actual installation and operation, and goodstability and economy, is sought. The grating interferometry system mayachieve the resolution of nanometer and sub-microradian and maysimultaneously measure two linear displacements and three rotations withsmall strokes. The interferometry system may effectively reduce theshortcomings of the distributed interferometry system in the applicationof the ultra-precision worktable and improve the performance of theultra-precision worktable of lithography machine. In addition, thegrating interferometry system may also be applied to scenarios wherelarge-stroke linear displacement and multi-degree-of-freedom measurementare required, for example, the precision measurement ofmulti-degree-of-freedom displacement of a worktable of a precisionmachine tool, a three-coordinate measuring machine, a semiconductortesting equipment, and so on.

The technical solution of the present disclosure is as follows:

A five-degree-of-freedom heterodyne grating interferometry system,including: a single-frequency laser 1 for emitting a single-frequencylaser light, the single-frequency laser light may be split into a beamof reference light and a beam of measurement light; an interferometerlens set 3 and a measurement grating 4 for converting the referencelight and the measurement light into a reference interference signal anda measurement interference signal; and multiple optical fiber bundles 5receiving the measurement interference signal and the referenceinterference signal respectively, wherein each of the optical fiberbundles 5 has multiple multimode optical fibers receiving interferencesignals at different positions on a same plane respectively.

Further, the reference interference signal includes one path ofreference interference signal, the measurement interference signalincludes two paths of measurement interference signals; the two paths ofmeasurement interference signals and the one path of referenceinterference signal are received via the optical fiber bundles 5respectively, each of the optical fiber bundles 5 has four multimodeoptical fibers for receiving interference signals at different positionson the same plane respectively, each of the optical fiber bundles 5outputs four optical signals, thus the total of the optical fiberbundles outputs twelve paths of optical signals.

Further, the measurement grating 4 may perform two-degree-of-freedomlinear motions in horizontal and vertical directions and three angularmotions with respect to the interferometer lens set 3.

Further, the interferometer lens set 3 sequentially includes, from oneside to the other side, a refractor 35, a refractive element 33, aquarter wave plate 34, a beam splitter prism 31 and a polarization beamsplitter prism 32, wherein the beam splitter prism 31 is disposed on thepolarization beam splitter prism 32.

Further, the reference light is split into three beams after beingincident to the beam splitter prism 31, and is used as reference lightsof three paths of interference signals after being reflected by thepolarization beam splitter prism 32.

The measurement light is split into three beams after being incident tothe beam splitter prism 31, wherein two beams of measurement light arereflected by the polarization beam splitter prism 32, are sequentiallyincident to the quarter wave plate 34 and the refractive element 33, andthen are incident to the measurement grating 4, diffracted by thegrating 4 and return along an original optical path, and are incident tothe polarization beam splitter prism 32 again and transmitted by thepolarization beam splitter prism 32, then interfere with two paths ofreference lights among the reference lights of the three paths ofinterference signals, thereby forming two paths of measurementinterference signals.

The other beam of measurement light is reflected by the polarizationbeam splitter prism 32, incident to the quarter wave plate 34, thenreturns along an original optical path after being reflected by thereflector 35, and is incident to the quarter wave plate 34 and thepolarization beam splitter prism 32 again and transmitted by thepolarization beam splitter prism 32, then interferes with the other pathof reference light among the reference lights of the three paths ofinterference signals, thereby forming one path of reference interferencesignal.

Further, components of the interferometer lens set 3 are closelyadjacent and fixed and are integrated into an integrated structure.

Further, a cross section of the refractive element 33 is an isoscelestrapezoid, and the measurement light is refracted when transmittedthrough both sides of the trapezoid and reflected when transmittedthrough a top of the trapezoid.

Further, after being incident to the refractive element 33, the twobeams of measurement light are incident to the measurement grating 4 inan incident light path at a specific angle, the specific angle makes adiffracted light path coincide with the incident light path, and thediffracted light path passes through the refractive element 33 tointerfere in parallel with two paths of reference lights among thereference lights of the three paths of interference signals, therebyforming two paths of measurement interference signals.

Further, the grating interferometry system further includes anacousto-optic modulator 2 for frequency shifting of the splitsingle-frequency laser.

Further, the grating interferometry system further includes aphotoelectric conversion unit 6 and an electronic signal processingcomponent 7, wherein: the photoelectric conversion unit 6 receives theoptical signals transmitted by the optical fiber bundles 5 and convertthe optical signals into electrical signals for input to the electronicsignal processing component 7.

the electronic signal processing component 7 receives the electricalsignals to calculate a linear displacement and/or an angular motion ofthe measurement grating 4.

Compared with the prior art, the five-degree-of-freedom heterodynegrating interferometry system provided by the present disclosure has thefollowing advantages.

(1) The interferometry system of the present disclosure can realizesimultaneous measurement of five-degree-of-freedom including twotranslational displacements and three rotation angles, and, whilegreatly improving the measurement efficiency, the environmentalsensitivity is low, the measurement signal is easy to process, and theresolution and precision can reach nanometers level or even higher.

(2) The interferometry system of the present disclosure has a small sizeand high integration, which effectively improves the space utilizationrate and the integration of the whole application system.

(3) Compared with the conventional multi-degree-of-freedominterferometry system, on the basis of meeting requirements of themeasurement accuracy, the interferometry system of the presentdisclosure can effectively avoid the influence of the geometricinstallation error between the interferometer and the motion unit insingle degree of freedom measurement.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects and results of the present disclosure willbecome more apparent and easier to be understood by the followingspecific embodiments and the claims with reference to the accompanyingdrawings.

FIG. 1 is a schematic view illustrating the five-degree-of-freedomheterodyne grating interferometry system of the present disclosure.

FIG. 2 is a schematic view illustrating the structure of theinterferometer lens set of the present disclosure.

FIG. 3 is a schematic view illustrating an optical fiber bundle of thepresent disclosure.

FIG. 4 is a schematic view illustrating FIG. 3 of the present disclosurein direction A.

REFERENCE NUMERALS

-   -   1: single-frequency laser;    -   2: acousto-optic modulator;    -   3: interferometer lens set;    -   4: measurement grating;    -   5: optical fiber bundle;    -   6: photoelectric conversion unit;    -   7: electronic signal processing component;    -   31: beam splitter prism;    -   32: polarization beam splitter prism;    -   33: refractive element;    -   34: quarter wave plate; and    -   35: reflector.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The technical solutions of the present disclosure will be clearly andcompletely described below in conjunction with the accompanyingdrawings. Obviously, the embodiments described herein are only part ofthe embodiments of the present disclosure, rather than all of them.Based on the embodiments of the present disclosure, all otherembodiments obtained by those of ordinary skill in the art withoutcreative work shall fall within the protection scope of the presentdisclosure.

In the description of the present disclosure, it should be noted thatthe orientation or positional relationship indicated by terms such as“center”, “upper”, “lower”, “left”, “right”, “vertical”, “horizontal”,“inside” and “outside” is based on the orientation or positionalrelationship shown in the drawings, which is merely for the convenienceof describing the present disclosure and simplifying the description,rather than indicating or implying that the indicated device or elementmust have a specific orientation or be configured and operated in aspecific orientation, and therefore should not be understood as alimitation to the present disclosure. Further, terms such as “first”,“second” and “third” are only used for the purpose of description andshould not be understood as indicating or implying relative importance.

In the description of the present disclosure, it should be noted thatterms such as “install”, “connect” and “couple” should be understood ina broad sense, unless otherwise explicitly specified and limited. Forexample, components may be fixedly connected, detachably connected orintegrally connected; may be mechanically connected or electricallyconnected; may be directly connected, or may be indirectly connectedthrough an intermediate medium, and there may be an internalcommunication between two components. For those of ordinary skill in theart, the specific meanings of the above terms in the present disclosurecan be understood according to specific circumstances.

FIG. 1 is a schematic view illustrating the five-degree-of-freedomheterodyne grating interferometry system of the present disclosure. Asshown in FIG. 1 , the five-degree-of-freedom heterodyne gratinginterferometry system includes a single-frequency laser 1, anacousto-optic modulator 2, an interferometer lens set 3, a measurementgrating 4, optical fiber bundles 5, a photoelectric conversion unit 6,and an electronic signal processing component 7. Preferably, themeasurement grating 4 is a one-dimensional reflection type grating.

FIG. 2 is a schematic view illustrating the structure of theinterferometer lens set of the present disclosure. As shown in FIG. 2 ,the interferometer lens set 3 includes, in order from one side to theother side (in FIG. 2 , from left side to right side, or from a sideclose to the measurement grating 4 to the other side): a reflector 35, arefractive element 33, a quarter wave plate 34, a beam splitter prism31, and a polarization beam splitter prism 32. The beam splitter prism31 is disposed on the polarization beam splitter prism 32, that is, thebeam splitter prism 31 is disposed on an upper portion of theinterferometer lens set, the polarization beam splitter prism 32 isdisposed on a lower portion of the interferometer lens set, and therefractive element 33 is disposed near the top of one side of theinterferometer lens set (in FIG. 2 , near the top on the left side). Toachieve a high degree of integration, preferably, components of theinterferometer lens set 3 are fixed compactly and adjacently and areintegrated into an integrated structure, and more preferably, thecomponents are fixed by bonding.

FIG. 3 is a schematic view illustrating an optical fiber bundle of thepresent disclosure, and FIG. 4 is a schematic view illustrating FIG. 3of the present disclosure in direction A. As shown in FIGS. 3 and 4 ,each of the optical fiber bundles 5 includes four multimode opticalfibers, which are disposed at different positions in the same plane,used to receive interference signals at different spatial positions, andfour independent optical signals are generated via optical fibertransmission.

The principle of the grating interferometry system will be explained indetail with reference to FIG. 1 and FIG. 2 , specifically:

The single-frequency laser 1 emits a single-frequency light, thesingle-frequency light is coupled by the optical fiber, split by a beamsplitter, and then is incident to the acousto-optic modulator 2 forfrequency shifting, and after collimated by the Green lens, two paths ofpolarized lights (s light) with frequency difference are obtained, onepath of which is used as a reference light and the other path as ameasurement light.

The reference light is split twice by the upper portion of the beamsplitter prism 31, then three beams of laser are obtained, which areused as reference lights of the three paths of interference signalsafter being incident downward and reflected by the polarization beamsplitter prism.

The measurement light is split by the beam splitter prism 31 and alsoobtains three beams of laser incident downward. Two beams thereof arereflected by the polarization beam splitter prism 32, then are incidentto the quarter wave plate 34 and deflected by the refractive element 33sequentially, and then are incident to the measurement grating 4, and,after being diffracted by the grating, ±1 orders diffracted lightsinclude the rotation angle and displacement information of the grating,the two beams return along an original optical path, and are incident tothe quarter wave plate 34 and the polarization beam splitter prism 32again and transmitted by the polarization beam splitter prism 32, theninterfere with the reference lights, thereby forming two paths ofmeasurement interference signals. The other beam thereof is reflected bythe polarization beam splitter prism 32, then is incident to the quarterwave plate 34 and reflected by the reflector 35 sequentially, andreturns along an original optical path, and is incident to the quarterwave plate 34 and the polarization beam splitter prism 32 again and istransmitted by the polarization beam splitter prism 32, then interferewith the reference light, thereby forming a reference interferencesignal.

Preferably, the light path of the present disclosure is arranged inLittrow type, that is, the measurement lights are deflected after beingincident to the refractive element 33, and the deflected measurementlights are incident to the measurement grating 4 at a specific anglesuch that the diffracted light path coincides with the incident lightpath, and the diffracted light path passes through the refractiveelement 33 and forms the measurement light parallel to the referencelight, then the lights are incident to the quarter wave plate 34 and thepolarization beam splitter prism 32 again and transmitted by thepolarization beam splitter prism 32, to interfere with the referencelights, thereby forming two paths of measurement signals.

The two paths of measurement interference signals and one path ofreference interference signal are received by three optical fiberbundles 5 respectively. Each of the optical fiber bundles includes fourmultimode optical fibers therein for collecting optical signals of thesame interference signal at different spatial positions. There are atotal of twelve optical fibers and there form a total of twelve paths ofsignals, which are transmitted to the photoelectric conversion unit 6 tobe converted into electrical signals and input to the electronic signalprocessing component 7 for processing. Using the obtained phaseinformation, information about rotation angle of the grating may becalculated based on the differential wavefront principle, themeasurement of three rotation angles may be realized at the same time. Aphase caused by the additional displacement is compensated according tothe obtained rotation angle, and the linear motion with two degrees offreedom is solved. When the measurement grating 4 performstwo-degree-of-freedom linear motions in horizontal and verticaldirections and three angular motions with respect to the interferometerlens set 3, the electronic signal processing component 7 will outputtwo-degree-of-freedom linear displacement and angular motion.

The expression of the five-degree-of-freedom motion calculation is asfollows:

$\theta_{x} = \frac{\left( {\phi_{1} + \phi_{2} + \phi_{5} + \phi_{6}} \right) - \left( {\phi_{3} + \phi_{4} + \phi_{7} + \phi_{8}} \right)}{\Gamma_{x}}$$\theta_{y} = \frac{\left( {\phi_{1} + \phi_{3} + \phi_{5} + \phi_{7}} \right) - \left( {\phi_{2} + \phi_{4} + \phi_{6} + \phi_{8}} \right)}{\Gamma_{y}}$$\theta_{z} = \frac{\left( {\phi_{1} + \phi_{2} + \phi_{7} + \phi_{8}} \right) - \left( {\phi_{3} + \phi_{4} + \phi_{5} + \phi_{6}} \right)}{\Gamma_{z}}$$x = {\left\lbrack {\frac{\left( {\phi_{1} + \phi_{2} + \phi_{3} + \phi_{4}} \right) - \left( {\phi_{5} + \phi_{6} + \phi_{7} + \phi_{8}} \right)}{4} + \phi_{x\theta}} \right\rbrack \times \frac{p}{4\pi}}$$z = {\left\lbrack {\frac{\left( {\phi_{1} + \phi_{2} + \phi_{3} + \phi_{4}} \right) + \left( {\phi_{5} + \phi_{6} + \phi_{7} + \phi_{8}} \right)}{4} + \phi_{z\theta}} \right\rbrack \times \frac{\lambda}{8\pi\cos\theta}}$

Wherein, θ_(x,y,z) are rotation angles of the grating, x, z are gratingdisplacements, ϕ_(1,2,3,4,5,6,7,8) are electronic signal processing cardreadings, Γ_(x,y,z) are calibration constants, ϕ_(xθ,zθ) are additionaldisplacement compensation phases, p is a grating pitch, 2 is a laserwavelength, and B is a Littrow angle.

The interferometry system and structure scheme provided in the aboveembodiments can realize simultaneous measurement of three rotationaldegrees of freedom and two linear degrees of freedom, and the system hasa short measurement optical path and is minimally affected by theenvironment. The interferometry system using optical fiber bundles mayeffectively reduce the number of system components, improve theanti-interference ability and system integration of the system, it iseasy to process the measurement signal, and the measurement resolutionof the rotation angle can reach microradians, the measurement resolutionof the linear displacement can reach nm level; also, the gratinginterferometer system has advantages such as simple structure, smallsize, light weight, easy installation and arrangement, convenientapplication. When the system is applied to the displacement measurementof an ultra-precision worktable of lithography machine, compared withthe laser interferometer measurement system, it can effectively reducethe volume and mass of the worktable on the basis of meeting themeasurement requirements, greatly improve the dynamic performance of theworktable, and thus comprehensively improve the overall performance ofthe worktable. The five-degree-of-freedom heterodyne gratinginterferometry system may also be applied to precision measurement ofmulti-degree-of-freedom displacements of worktable of a precisionmachine tool, a three-coordinate measuring machine, a semiconductortesting equipment, etc. Six-degree-of-freedom ultra-precisionmeasurement may be achieved by arranging multiple five-degree-of-freedominterferometry system and using redundant information, thereby meetingthe needs of a worktable of lithography machine forsix-degree-of-freedom position and attitude measurement.

Although the foregoing disclosure shows exemplary embodiments of thepresent disclosure, it should be noted that various changes andmodifications can be made without departing from the scope defined bythe claims. In addition, although the elements of the present disclosuremay be described or required in individual forms, it is also conceivableto have multiple elements, unless explicitly limited to a singleelement.

What is claimed is:
 1. A five-degree-of-freedom heterodyne gratinginterferometry system, comprising: a single-frequency laser for emittinga single-frequency laser light, the single-frequency laser light issplit into a beam of reference light and a beam of measurement light; aninterferometer lens set and a measurement grating for converting thereference light and the measurement light into a reference interferencesignal and a measurement interference signal; and multiple optical fiberbundles receiving the measurement interference signal and the referenceinterference signal respectively, wherein each of the optical fiberbundles has multiple multimode optical fibers receiving interferencesignals at different positions on a same plane respectively; wherein thereference interference signal comprises one path of the referenceinterference signal, the measurement interference signal comprises twopaths of the measurement interference signals, the two paths ofmeasurement interference signals and the one path of the referenceinterference signal are received via the optical fiber bundlesrespectively, and wherein each of the optical fiber bundles has fourmultimode optical fibers for receiving interference signals at differentpositions on the same plane respectively, each of the optical fiberbundles outputs four optical signals, thus a total of the optical fiberbundles outputs twelve paths of optical signals.
 2. The gratinginterferometry system according to claim 1, wherein the measurementgrating performs two-degree-of-freedom linear motions in horizontal andvertical directions and three angular motions, with respect to theinterferometer lens set.
 3. The grating interferometry system accordingto claim 1, wherein the interferometer lens set sequentially comprises,from one side to another side, a refractor, a refractive element, aquarter wave plate, a beam splitter prism and a polarization beamsplitter prism, wherein the beam splitter prism is disposed on thepolarization beam splitter prism.
 4. The grating interferometry systemaccording to claim 3, wherein: the reference light is split into threebeams after being incident to the beam splitter prism, and is used asreference lights of three paths of interference signals after beingreflected by the polarization beam splitter prism; the measurement lightis split into three beams after being incident to the beam splitterprism, wherein two of the three beams of the measurement light arereflected by the polarization beam splitter prism, are sequentiallyincident to the quarter wave plate and the refractive element, and thenare incident to the measurement grating, diffracted by the grating andreturn along an original optical path, and are incident to thepolarization beam splitter prism again and transmitted by thepolarization beam splitter prism, and then interfere with two paths ofreference lights among the reference lights of the three paths ofinterference signals, thereby forming two paths of measurementinterference signals; and the remaining one of the three beams ofmeasurement light beam is reflected by the polarization beam splitterprism, incident to the quarter wave plate, and then returns along anoriginal optical path after being reflected by the refractor, and isincident to the quarter wave plate and the polarization beam splitterprism again and transmitted by the polarization beam splitter prism, andthen interferes with the other path of reference light among thereference lights of the three paths of interference signals, therebyforming one path of reference interference signal.
 5. The gratinginterferometry system according to claim 4, wherein after being incidentto the refractive element, the two beams of measurement light areincident to the measurement grating in an incident light path at aspecific angle, the specific angle makes a diffracted light pathcoincide with the incident light path, and the diffracted light pathpasses through the refractive element to interfere in parallel with twopaths of reference lights among the reference lights of the three pathsof interference signals, thereby forming two paths of measurementinterference signals.
 6. The grating interferometry system according toclaim 3, wherein components of the interferometer lens set are closelyadjacent and fixed and are integrated into an integrated structure. 7.The grating interferometry system according to claim 3, wherein a crosssection of the refractive element is an isosceles trapezoid, whereinupon transmission of the measurement light through both sides of thetrapezoid, the measurement light is refracted, and upon transmission ofthe measurement light through a top of the trapezoid, the measurementlight is reflected.
 8. The grating interferometry system according toclaim 1, further comprising: an acousto-optic modulator for frequencyshifting of the split single-frequency laser.
 9. The gratinginterferometry system according to claim 1, further comprising: aphotoelectric conversion unit and an electronic signal processingcomponent, wherein: the photoelectric conversion unit receives theoptical signals transmitted by the optical fiber bundle and converts theoptical signals into electrical signals, and inputs the electricalsignals to the electronic signal processing component; the electronicsignal processing component receives the electrical signals to calculateone or both of a linear displacement and an angular motion of themeasurement grating.